Abstract
A continuum model of perfect or dislocated crystals is considered, and it is shown how one can view such a crystalline medium as an oriented medium, and as a material manifold with an irrotational law of distant parallelism. In dislocated crystals with twist, the Burgers vectors of homologous cycles are not independent of the cycles unless the amount of twist is restricted.
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References
Cf. Love, A. E. H.: The Mathematical Theory of Elasticity, Fourth Edition, Appendix to Chaps. VIII and IX. New York: Dover Publications 1927.
Cosserat, E., and F. Cosserat: Théorie des Corps Déformable. Paris: Hermann 1909.
Günther, W.: Zur Statik und Kinematik des Cosseratschen Kontinuums. Abh. d. Braunschweigischen Wiss. Ges. 10, 195 (1958).
Fox, N.: A Continuum Theory of Dislocations for Single Crystals. J. Inst. Maths. Appl. 2, 285 (1966).
Noll, W.: Materially Uniform Simple Bodies with Inhomogenities, Report 67–26, Dept. of Math., Carnegie Inst, of Tech. 1967.
Whitney, H.: Geometric Integration Theory. Princeton University Press 1957.
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© 1968 Springer-Verlag Berlin · Heidelberg
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Toupin, R.A. (1968). Dislocated and Oriented Media. In: Continuum Theory of Inhomogeneities in Simple Bodies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85992-2_2
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DOI: https://doi.org/10.1007/978-3-642-85992-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-85994-6
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